Lab
Flux Concentrator Core Geometry Lab
How much of a toroidal core you actually need, and what you give up by removing part of it — an illustrative exploration of the four sensor-core shapes studied in a real published paper, not a design tool.
Core geometry
Estimated saturation current
40.0 A
1.0× the closed ring's own 40.0 A
Core covers
100.0% of the loop
Core material length
251.3 mm
Open path length
0.0 mm
Total reluctance
1,000 kA·t/Wb
What the real paper actually measured
This lab estimates only the DC saturation-current trend from reluctance — not sensor sensitivity. The numbers below are the paper's own FEM-simulated, transient sensitivity results, printed here for comparison, not computed by this tool.
| Core geometry | Sensitivity vs. closed core | Material usage |
|---|---|---|
| HFCT (closed ring) | 100% | 100% |
| HFCT with small air gap | 84% | 125% |
| Standard flux concentrator (half-core) | 57% (up to 89% optimally positioned) | 89% |
| Small flux concentrator (120° sector) | 39% (up to 139% optimally positioned) | 139% |
How this is built, and its real limit: the toroid's mean circumference is split by a single coverage fraction — the covered part is ordinary core material, the uncovered part is treated as an equivalent straight air path of the same length and cross-section, solved with the same reluctance network as the Transformer & Magnetic Circuit Designer tool. That straight-air-path assumption is a reasonable stand-in for a small gap (a few mm, where fringing is a modest, well-understood correction), but for the half-core and sector cases — where most of the loop is open — it stops being a small correction and becomes the dominant, unverified assumption: the real field could spread into a much larger effective area than a neat rod of core cross-section, or take a shorter path through open space, or both, and this simple model has no way to know which. We don't claim a direction for that error here, only that it exists and can be large. This is exactly why the source paper used full 3D finite-element simulation for these open shapes instead of a hand calculation — a 1D reluctance network is not built for geometry this asymmetric. Treat the numbers above as showing the right trend (less core material means a higher saturation threshold), not a design figure.
Further reading
- B. Zimmer, C. F. Hermosilla Morales, F. Jenau, "Theoretical study of design aspects of inductive partial discharge sensors with focus on the novel flux concentrator concept," 2025 60th International Universities Power Engineering Conference (UPEC), IEEE.
- Reuses the same reluctance-network engine as the Transformer & Magnetic Circuit Designer tool — see that tool for the underlying magnetic-circuit theory and its own references.